Mathematical Programs with Equilibrium Constraints: Automatic Reformulation and Solution via Constrained Optimization

Ferris, Michael C.; Dirkse, Steven P.; Meeraus, Alexander

doi:10.1017/cbo9780511614330.005

Cited by 56 publications

(45 citation statements)

References 47 publications

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“…Numerical Results. We tried our algorithm on two test-sets: the MacMPEC test-set already mentioned (found at [13]), and a testset, described in [5], of pure complementarity problems which have usually been regarded as difficult for complementarity solvers. We were able to solve almost all the problems successfully.…”

Section: Numerical Experience With Mpecsmentioning

confidence: 99%

Interior-Point Algorithms, Penalty Methods and Equilibrium Problems

Benson

Sen

Shanno

et al. 2006

Comput Optim Applic

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Abstract. In this paper we consider the question of solving equilibrium problems-formulated as complementarity problems and, more generally, mathematical programs with equilibrium constraints (MPECs)-as nonlinear programs, using an interior-point approach. These problems pose theoretical difficulties for nonlinear solvers, including interior-point methods. We examine the use of penalty methods to get around these difficulties and provide substantial numerical results. We go on to show that penalty methods can resolve some problems that interior-point algorithms encounter in general.

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Section: Numerical Experience With Mpecsmentioning

confidence: 99%

Interior-Point Algorithms, Penalty Methods and Equilibrium Problems

Benson

Sen

Shanno

et al. 2006

Comput Optim Applic

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“…The test problems come from the MacMPEC test suite by Leyffer ([13]) and the set described in [5] by Ferris, and all were formulated in ampl. All testing was conducted on a Dell Workstation running Red Hat Linux 9 with 5GB of main memory and 864MHz clock speed.…”

Section: Resultsmentioning

confidence: 99%

Interior-Point Algorithms, Penalty Methods and Equilibrium Problems

Benson¹,

Sen²,

Shanno³

et al. 2004

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“…For our calculations, we use the GAMS NLPEC solver, with CONOPT 3 as the subsolver (Ferris et al, 2005).…”

Section: Methodsmentioning

confidence: 99%

Imperfect Cartelization in OPEC

Okullo

Reynès

2016

SSRN Journal

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A model of global oil production is applied to study cartelization by OPEC countries. Writing out the shadow price on quota allocations so as to draw correspondence to coefficients of cooperation (Cyert et al. 1973), we examine the incentives that different OPEC members to collude. We find that heterogeneity in OPEC and the supplies of the non-OPEC fringe create strong incentives against OPEC cooperation. OPEC's optimal supply strategy although observed to be substantially more restrictive than that of a Cournot-Nash oligopoly, is found to still be more accommodative than that of a perfect cartel. The strategy involves allocating larger than proportionate quotas to smaller and relatively costlier producers as if to bribe their participation in the cartel. This is contrary to predictions of the standard cartel model that such producers should be allocated relatively more stringent quotas.Furthermore, we find that cartel collusion is likely to be sustained for elastic than inelastic demand. Since global oil demand is well known to be inelastic, this observation provides another structural explanation for why OPEC behavior is inconsistent with that of a perfect cartel. Our study points to multiple headwinds that limit OPECs ability to raise long-run global oil prices.

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Mathematical Programs with Equilibrium Constraints: Automatic Reformulation and Solution via Constrained Optimization

Cited by 56 publications

References 47 publications

Interior-Point Algorithms, Penalty Methods and Equilibrium Problems

Interior-Point Algorithms, Penalty Methods and Equilibrium Problems

Interior-Point Algorithms, Penalty Methods and Equilibrium Problems

Imperfect Cartelization in OPEC

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